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Obtaining the efficient set of nonlinear biobjective optimization problems via interval branch-and-bound methods

COMPUTATIONAL OPTIMIZATION AND APPLICATIONS 2009年第3期42卷 393-419页

作者： Fernandez, Jose Toth, Boglarka Univ Murcia Dpt Stat & Operat Res Murcia Spain Budapest Univ Technol & Econ Dpt Differential Equat H-1117 Budapest Hungary

Obtaining a complete description of the efficient set of multiobjective optimization problems can be of invaluable help to the decision-maker when the objectives conflict and a solution has to be chosen. In this paper we present an interval branch-and-bound algorithm which aims at obtaining a tight outer approximation of the whole efficient set of nonlinear biobjective problems. The method enhances the performance of a previous rudimentary algorithm thanks to the use of new accelerating devices, namely, three new discarding tests. Some computational studies on a set of competitive location problems demonstrate the efficiency of the discarding tests, as well as the superiority of the new algorithm, both in time and in quality of the outer approximations of the efficient set, as compared to another method, an interval constraint-like algorithm, with the same aim. Furthermore, we also give some theoretical results of the method, which show its good properties, both in the limit (when the tolerances are set equal to zero and the algorithm does not stop) and when the algorithm stops after a finite number of steps (when we use positive tolerances). A key point in the approach is that, thanks to the use of interval analysis tools, it can be applied to nearly any biobjective problem.

关键词： Nonlinear biobjective optimization Efficient set Outer approximation Interval analysis branch-and-bound method Discarding tests Continuous location

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A hybrid approach combining interior-point and branchand-bound methods applied to the problem of sugar cane waste

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JOURNAL OF THE OPERATIONAL RESEARCH SOCIETY 2017年第2期68卷 147-164页

作者： de Lima, Camila Balbo, Antonio Roberto Donadon Homem, Thiago Pedro Florentino Silva, Helenice de Oliveira Univ Sao Paulo Postgrad Program Comp Sci & Computat Math ICMC Ave Trabalhador Sao Carlense400 BR-13566590 Sao Carlos SP Brazil UNESP Sao Paulo State Univ Dept Math FC Ave Engenheiro Luiz Edmundo Carrijo Coube14-01 BR-17033360 Bauru SP Brazil IFSP Sao Paulo Fed Inst Educ Sci & Technol Ave Zelia de Lima Rosa100 BR-18550000 Boituva SP Brazil UNESP Sao Paulo State Univ Dept Biostat IBB Distrito Rubiao Jr S-N BR-18618970 Botucatu SP Brazil

This paper proposes a hybrid approach for solving themulti-objective model related to theminimisation of sugar cane waste collection costs and/or the maximisation of produced energy by this waste, with the aid of strategies for solving multi-objective problems, which transform the problem into a set of single-objective problems. This approach combines the predictor-corrector primal-dual interior-point and branch-and-bound methods in order to solve these single-objective problems. The model consists in identifying the sugar cane varieties with the lowest waste collection costs, while simultaneously it aims to obtain the greatest amount of produced energy by this waste. The hybrid methods are implemented in C++ programming language, and tests are performed to determine the efficient solutions in Pareto optimal sense of the multi-objective model and compare the performance of the hybrid method using the integrality test and without considering it. The mathematical results confirm that the proposed hybrid method for solving the aforementioned models presents good computational performance and reliable solutions.

关键词： integer programming predictor-corrector primal-dual interior-point method branch-and-bound method sugarcane waste multi-objective model

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Multisection in interval branch-and-bound methods for global optimization -: I.: Theoretical results

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JOURNAL OF GLOBAL OPTIMIZATION 2000年第4期16卷 371-392页

作者： Csallner, AE Csendes, T Markót, MC Juhasz Gyula Teachers Training Coll Dept Comp Sci Szeged Hungary Attila Jozsef Univ Dept Appl Informat Szeged Hungary Attila Jozsef Univ Inst Informat Szeged Hungary

We have investigated variants of interval branch-and-bound algorithms for global optimization where the bisection step was substituted by the subdivision of the current, actual interval into many subintervals in a single iteration step. The convergence properties of the multisplitting methods, an important class of multisection procedures are investigated in detail. We also studied theoretically the convergence improvements caused by multisection on algorithms which involve the accelerating tests (like e.g. the monotonicity test). The results are published in two papers, the second one contains the numerical test result.

关键词： branch-and-bound method global optimization interval arithmetic multisection accelerating devices

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Solving the sum-of-ratios problem by a stochastic search algorithm

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JOURNAL OF GLOBAL OPTIMIZATION 2008年第1期42卷 91-109页

作者： Wu, Wei-Ying Sheu, Ruey-Lin Birbil, S. Ilker Natl Cheng Kung Univ Dept Math Tainan 701 Taiwan Michigan State Univ Dept Stat & Probabil E Lansing MI 48824 USA Sabanci Univ Fac Engn & Nat Sci TR-34956 Istanbul Turkey

In spite of the recent progress in fractional programming, the sum-of-ratios problem remains untoward. Freund and Jarre proved that this is an NP-complete problem. Most methods overcome the difficulty using the deterministic type of algorithms, particularly, the branch-and-bound method. In this paper, we propose a new approach by applying the stochastic search algorithm introduced by Birbil, Fang and Sheu to a transformed image space. The algorithm then computes and moves sample particles in the q - 1 dimensional image space according to randomly controlled interacting electromagnetic forces. Numerical experiments on problems up to sum of eight linear ratios with a thousand variables are reported. The results also show that solving the sum-of-ratios problem in the image space as proposed is, in general, preferable to solving it directly in the primal domain.

关键词： sum-of-ratios problems min-max problems Dinkelbach-type method branch-and-bound method stochastic search method

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SYMMETRIC MINIMAL COVERING PROBLEM AND MINIMAL PLAS WITH SYMMETRIC VARIABLES

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IEEE TRANSACTIONS ON COMPUTERS 1985年第6期34卷 523-541页

作者： YOUNG, MH MUROGA, S UNIV ILLINOIS DEPT COMP SCIURBANAIL 61801

This paper first discusses the symmetric property of the minimal covering problem in terms of group theory and then the use of this property in the branch-and-bound method for solving the problem. Computational results on solving sample problems are shown to demonstrate the improvement of computational efficiency of the branch-and-bound method by the utilization of the symmetric property. The sample problems contain the minimal sum derivation of symmetric switching functions, as an application to the design of minimal programmable logic arrays (PLA"s). It is shown that when the minimal covering problem derived for the given switching function has symmetric permutations, the given switching function may not be symmetric; although when the given switching function is symmetric, the minimum covering problem obtained from the function is symmetric. The branch-and-bound method based on the symmetric property can be applied not only to symmetric switching functions but also to switching functions which are not symmetric, if the corresponding minimal covering problems have symmetric permutations. The method can be also applied to minimal covering problems which arise outside the minimal sum derivation problems for switching functions.

关键词： branch-and-bound method minimal covering problem minimal sum permutation group programmable logic array symmetric function symmetric permutation

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A complementarity-based partitioning and disjunctive cut algorithm for mathematical programming problems with equilibrium constraints

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JOURNAL OF GLOBAL OPTIMIZATION 2006年第1期36卷 89-114页

作者： Judice, Joaquim J. Sherali, Hanif D. Ribeiro, Isabel M. Faustino, Ana M. Univ Coimbra Dept Matemat P-3000 Coimbra Portugal Inst Telecomunicacoes Coimbra Portugal Virginia Polytech Inst & State Univ Grado Dept Ind & Syst Engn Blacksburg VA 24061 USA Univ Porto Fac Engn Dept Civil Engn Seccao Matemat P-4100 Oporto Portugal

In this paper a branch-and-bound algorithm is proposed for finding a global minimum to a Mathematical Programming Problem with Complementarity (or Equilibrium) Constraints (MPECs), which incorporates disjunctive cuts for computing lower bounds and employs a Complementarity Active-Set Algorithm for computing upper bounds. Computational results for solving MPECs associated with Bilivel Problems, NP-hard Linear Complementarity Problems, and Hinge Fitting Problems are presented to highlight the efficacy of the procedure in determining a global minimum for different classes of MPECs.

关键词： active-set algorithm branch-and-bound method complementarity disjunctive cuts global optimization

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A branch-and-bound algorithm for the mini-max spanning forest problem

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 1997年第1期101卷 93-103页

作者： Yamada, T Takahashi, H Kataoka, S Department of Computer Science The National Defense Academy Yokosuka Kanagawa 239 Japan

The mini-max spanning forest problem requires to find a spanning forest of an undirected graph that minimizes the maximum of the costs of constituent trees. In a previous work we proved this problem NP-hard. In the current paper we present three lower bounds for this problem and develop a branch-and-bound algorithm to solve the problem exactly. The algorithm is implemented and numerical experiments are conducted on a series of test problems. The experiments compare the performances of the proposed bounds and search strategies in the algorithm as well as investigate the effects of instance characteristics on the behavior of the algorithm. Also, extension of the problem to the case of more than two root vertices as well as to the problem of determining the root locations are discussed. (C) 1997 Elsevier Science B.V.

关键词： spanning forest mini-max problem branch-and-bound method graph theory

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On-orbit assembly mission planning considering topological constraint and attitude disturbance

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ACTA ASTRONAUTICA 2018年 152卷 692-704页

作者： She, Yuchen Li, Shuang Du, Bin Cao, Kai Nanjing Univ Aeronaut & Astronaut Coll Astronaut Nanjing 210016 Jiangsu Peoples R China Nanjing Univ Aeronaut & Astronaut Adv Space Technol Lab Nanjing 210016 Jiangsu Peoples R China Dept Astronaut Engn Nanjing Jiangsu Peoples R China

This paper investigates the on-orbit assembly mission planning problem of a large space antenna structure. The study is significantly important for the construction of large-scale spatial structures. The flexible connection between the antenna pieces and the topological constraint are taken into consideration. Several innovative approaches are presented to realize the mission planning process. First, the mesh model from the fly net dynamics is adopted and modified to create a mapping between the vibrations of the antenna plate during the assembly process and the assembly path. Second, the geometrical model is developed to implement the topological constraint into the system. Finally, a hybrid method combining the branch-and-bound method and the modified ant colony algorithm is proposed to solve the optimization problem. The simulation results show that the proposed algorithm can efficiently obtain a solution which respects the topological constraint and suppresses the vibration disturbance as much as possible.

关键词： On-orbit assembly Vibration suppression Mission planning Topological constraint branch-and-bound method

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Optimal scheduling of a two-stage hybrid flow shop

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MATHEMATICAL methodS OF OPERATIONS RESEARCH 2006年第1期64卷 107-124页

作者： Haouari, Mohamed Hidri, Lotfi Gharbi, Anis Ecole Polytechn Tunisie Combinatorial Optimizat Res Grp ROI La Marsa 2078 Tunisia

We present an exact branch-and-bound algorithm for the two-stage hybrid flow shop problem with multiple identical machines in each stage. The objective is to schedule a set of jobs so as to minimize the makespan. This is the first exact procedure which has been specifically designed for this strongly NP-hard problem. Among other features, our algorithm is based on the exact solution of identical parallel machine scheduling problems with heads and tails. We report the results of extensive computational experiments on instances which show that the proposed algorithm solves large-scale instances in moderate CPU time.

关键词： deterministic scheduling hybrid flow shop branch-and-bound method

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Global optimization of robust truss topology via mixed integer semidefinite programming

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OPTIMIZATION AND ENGINEERING 2010年第3期11卷 355-379页

作者： Yonekura, Kazuo Kanno, Yoshihiro Univ Tokyo Dept Math Informat Grad Sch Informat Sci & Technol Bunkyo Ku Tokyo 1138656 Japan

This paper discusses a global optimization method of robust truss topology under the load uncertainties and slenderness constraints of the member cross-sectional areas. We consider a non-stochastic uncertainty of the external load, and attempt to minimize the maximum compliance corresponding to the most critical load. A design-dependent uncertainty model in the external load is proposed in order to consider the variation of truss topology rigorously. It is shown that this optimization problem can be formulated as a 0-1 mixed integer semidefinite programming (0-1MISDP) problem. We propose a branch-and-bound method for computing the global optimal solution of the 0-1MISDP. Numerical examples illustrate that the topology of robust optimal truss depends on the magnitude of uncertainty. The presented method can provide global optimal solutions for benchmark examples, which can be used for evaluating the performance of any other local optimization method for robust structural optimization.

关键词： Topology optimization Robust optimization Semidefinite program Global optimization branch-and-bound method

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